Fractions · Add & subtract · 6.5

Simplify the result.

After adding or subtracting, always check whether the answer can be simplified — the final form should be in lowest terms.

01 / THE IDEA

See it work.

Watch the method

Simplify the result

1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.

1 / 4
16+13\frac{1}{6} + \frac{1}{3}
1

Find the LCD

The least common denominator of 6 and 3 is 6.

LCD(6,3)=6\text{LCD}(6,3)=6
2

Rewrite each fraction

Give both the LCD.

16+26\frac{1}{6} + \frac{2}{6}
3

Add the numerators

Keep the LCD.

36\frac{3}{6}
4

Simplify

Reduce to lowest terms.

12\frac{1}{2}
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a fraction like 3/4 or 1 1/2.

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— / WHY IT WORKS

The idea underneath.

Lowest-terms answers

A sum or difference often reduces. Always simplify the final fraction.

Why it works

Tidy the answer at the end.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Add 1/4 + 2/5

1

Find the LCD

The least common denominator of 4 and 5 is 20. \text{LCD}(4,5)=20

2

Rewrite each fraction

Give both the LCD. 5/20 + 8/20

3

Add the numerators

Keep the LCD. 13/20

EX 2medium

Add 3/4 + 2/3

1

Find the LCD

The least common denominator of 4 and 3 is 12. \text{LCD}(4,3)=12

2

Rewrite each fraction

Give both the LCD. 9/12 + 8/12

3

Add the numerators

Keep the LCD. 17/12

EX 3hard

Add 1/2 + 1/3

1

Find the LCD

The least common denominator of 2 and 3 is 6. \text{LCD}(2,3)=6

2

Rewrite each fraction

Give both the LCD. 3/6 + 2/6

3

Add the numerators

Keep the LCD. 5/6

04 / COMMON TRAPS

Where students slip.

Trap

Leaving 3/6 instead of 1/2.

Fix

Reduce the final answer.

Trap

Simplifying mid-way and losing track.

Fix

Combine first, then simplify.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Add 1/4 + 2/5

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
C2

Add 1/2 + 4/6

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
C3

Add 1/4 + 1/5

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
C4

Add 1/3 + 4/5

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
Apply

Apply (4)

A1

Add 3/4 + 2/3

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
A2

Add 2/3 + 1/5

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
A3

Add 1/3 + 1/6

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
A4

Add 2/3 + 2/5

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
Extension

Extension (4)

E1

Add 1/2 + 1/3

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
E2

Add 1/4 + 4/6

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
E3

Add 1/2 + 2/3

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.
E4

Add 1/2 + 1/3

Need a hint?
  • Combine, then simplify.
  • Check for a common factor in the result.